Abstract

This paper deals with the translation of first order formulas to predicate S5 formulas. This translation does not bring the first order formula itself to a modal system, but modal interpretation of the first order formula can be given by the translation. Every formula can be translated, and the additional condition such as formula's having only one variable, or having both world domain and individual domain is not required. I introduce an indexical predicate 'E' for the translation. The meaning that 'E(a)' is true is 'this world is 'a' '. Because of this meaning, I call 'E' an indexical predicate. 'E' plays an important role for the translation. In addition that the modal formulas can be translated into first order formulas, we can conclude that the first order logic and modal predicate logic isintertranslatable.